Question

You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its diameter to be 1.8�107m and its rotation period to be 22.3 hours. You have previously determined that the planet orbits 2.2�1011m from its star with a period of 402 earth days. Once on the surface you find that the free-fall acceleration is 12.2m/s2.
a. what is the mass of the Planet?
b. what is the mass of the star?

Answer 1

Answer

given,

diameter of planet = 1.8 x 10⁷ m

radius of planet = 0.9 x 10⁷ m

time period = 22.3 hours

the planet orbits 2.2 x 10¹¹ m   period of 402 earth days.

acceleration= 12.2 m/s²

we know

$g = \dfrac{GM_{p}}{r^2}$

$M_{p} = \dfrac{gr^2}{G}$

$M_{p} = \dfrac{12.2 \times (0.9 \times 10^7)^2}{6.67 \times 10^{-11}}$

M_p = 1.48 x 10²⁵  Kg

b) Formula to calculate the mass of star

$M_{s} = \dfrac{4\pi^2}{GT_s^2}(R^3)$

$M_{s} = \dfrac{4\pi^2}{6.67 \times 10^{-11} \times (402 \times 86400)^2}((2.2 \times 10^{11})^3)$

M_s = 5.22 x 10³³ Kg